TheATLASCollaboration

EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)

JHEP 04 (2021) 165

DOI:10.1007/JHEP04(2021)165

CERN-EP-2020-243 7th May 2021

Search for new phenomena in events with two opposite-charge leptons, jets and missing transverse momentum in 𝒑 𝒑 collisions at √

𝒔 = 13 TeV with the ATLAS detector

The ATLAS Collaboration

The results of a search for direct pair production of top squarks and for dark matter in events with two opposite-charge leptons (electrons or muons), jets and missing transverse momentum are reported, using 139 fb

of integrated luminosity from proton–proton collisions at

√ 𝑠=

13 TeV, collected by the ATLAS detector at the Large Hadron Collider during Run 2 (2015–2018).

This search considers the pair production of top squarks and is sensitive across a wide range of mass differences between the top squark and the lightest neutralino. Additionally, spin-0 mediator dark-matter models are considered, in which the mediator is produced in association with a pair of top quarks. The mediator subsequently decays to a pair of dark-matter particles.

No significant excess of events is observed above the Standard Model background, and limits are set at 95% confidence level. The results exclude top squark masses up to about 1 TeV, and masses of the lightest neutralino up to about 500 GeV. Limits on dark-matter production are set for scalar (pseudoscalar) mediator masses up to about 250

300

GeV.

arXiv:2102.01444v2 [hep-ex] 22 Apr 2021

1 Introduction

The Standard Model (SM) of particle physics is extremely successful in describing the phenomena of elementary particles and their interactions. Its predictive power has been proven with high precision by a wide range of experiments. However, despite its success, several important questions remain unanswered within the SM. One particularly striking omission is that it does not provide any explanation for dark matter (DM) [1, 2]. This is a non-baryonic, non-luminous matter component of the universe, for which there is strong evidence from a range of astrophysical observations. A weakly interacting dark-matter candidate particle can be produced at the Large Hadron Collider (LHC) [3] in a variety of ways, as described, for example, by supersymmetry (SUSY) [4–9] or DM models. At the LHC, one of the most promising modes is the production of DM particle pairs in association with on- or off-shell top quarks. Previous searches for DM candidates in association with a top quark pair have been performed by the ATLAS [10–16] and CMS [17–26] collaborations. However, those previous searches were statistically limited, or sensitive only up to limited particle masses. They also suffered from significant regions in which no limit could be placed because the kinematics of the decays made the signal events particularly difficult to identify.

This paper aims to extend the sensitivity beyond that of the previous searches to higher masses, and to cover the regions in which the previous ATLAS results had no sensitivity [27, 28]. It achieves this in part by exploiting a larger dataset, corresponding to 139 fb

of proton–proton collision data collected by the ATLAS experiment during Run 2 of the LHC (2015–2018) at a centre-of-mass energy

√

𝑠=

13 TeV.

Further improvements in sensitivity are obtained by using a new discriminating variable, the ‘object-based

T

significance’ [29], lowering the lepton

T

thresholds, and optimising a dedicated selection to target signal models in the most difficult kinematic regions.

Signal models and kinematic regions

For DM production, the simplified benchmark models [30–32] assume the existence of a mediator particle which couples both to the SM and to the dark sector [33–35]. The couplings of the mediator to the SM fermions are then severely restricted by precision flavour measurements. An ansatz that automatically relaxes these constraints is Minimal Flavour Violation [36]. This assumption implies that the interaction between any new neutral spin-0 state and SM matter is proportional to the fermion masses via Yukawa-type couplings.

It follows that colour-neutral mediators would be produced mainly through loop-induced gluon fusion or in association with heavy-flavour quarks. Here, the DM particles

are assumed to be pair produced through the exchange of a spin-0 mediator, which can be a colour-neutral scalar or pseudoscalar particle (denoted by

or

, respectively), in association with a top quark pair:

¯

¯ (Figure 1(a)).

Alternatively, dark-matter particles are also predicted in supersymmetry, a space-time symmetry that for each SM particle postulates the existence of a partner particle whose spin differs by one-half unit. To avoid violation of baryon number (

) and lepton number (

) conservation, a multiplicative quantum number

-parity [37], defined as

1

, is assumed to be conserved. SUSY particles are then produced in pairs, and the lightest supersymmetric particle (LSP) is stable and, if only weakly interacting, a candidate for dark matter [38, 39]. In the framework of a generic

-parity-conserving Minimal Supersymmetric Standard Model (MSSM) [40, 41], the supersymmetric scalar partners of right-handed and left-handed quarks (squarks), ˜

R

and ˜

L

, can mix to form two mass eigenstates, ˜

1

and ˜

2

, with ˜

1

defined

1Following Ref. [34], couplings to𝑊and𝑍bosons, as well as explicit dimension-4𝜙–ℎor𝑎–ℎcouplings, are set to zero in this simplified model. In addition, the coupling of the mediator to the dark sector is not taken to be proportional to the mass of the DM candidates.

t t

W W

φ/a b

νℓ χ χ ℓ ν

b (a)

t˜

t˜ W

p W p

˜ χ⁰₁

b `

ν

˜ χ⁰₁

b `

ν

(b)

˜t

˜t p

p

b `

ν

˜ χ⁰₁

b `

ν

˜ χ⁰₁

(c)

˜t

˜t

t W

t W

p p

˜ χ⁰₁

b `

ν

˜ χ⁰₁

b `

ν

(d)

Figure 1: Diagrams representing the signal models targeted by the searches: (a) the spin-0 mediator models, where the mediator decays into a pair of dark-matter particles and is produced in association with a pair of top quarks (𝑝 𝑝→ 𝜒𝜒𝑡¯ 𝑡¯), (b) the three-body ˜𝑡

1decay mode into an on-shell𝑊 boson, a 𝑏-quark and the lightest neutralino (˜𝑡₁→𝑏𝑊𝜒˜⁰

1), (c) the four-body ˜𝑡₁decay mode (˜𝑡₁→𝑏ℓ 𝜈¯ 𝜒˜⁰

1) where ¯ℓand𝜈are a anti-lepton with its neutrino and (d) the two-body ˜𝑡

1decay into an on-shell top quark and the lightest neutralino (˜𝑡

1 →𝑡𝜒˜⁰

1). For all the diagrams (a-d) the distinction between particle and anti-particle is omitted.

to be the lighter one. In the case of the supersymmetric partner of the top quark, ˜

, large mixing effects can lead to one of the top squark mass eigenstates, ˜

1

, being significantly lighter than the other squarks.

The charginos and neutralinos are mixtures of the bino, winos and Higgsinos that are superpartners of the U(1) and SU(2) gauge bosons and the Higgs bosons, respectively. Their mass eigenstates are referred to as ˜

𝑖 (𝑖=

1

2

and ˜

𝑗 (𝑗 =

1

2

3

4

in order of increasing mass. In a large variety of models, the LSP, which is the DM candidate, is the lightest neutralino ˜

1

. Searches for direct pair production of the top squark and DM particles can be performed in final states with two leptons (electrons or muons) of opposite electric charge, jets and missing transverse momentum (Figures 1(b)–1(d)). Depending on the mass difference between the top squark and the lighter SUSY particles, different decay modes are relevant.

For

˜

1) −𝑚(𝜒

˜

1) < 𝑚(𝑡)

, the three-body decay ˜

1→𝑏𝑊𝜒

˜

1

occurs through an off-shell top quark (Figure 1(b)). For smaller mass differences, i.e.

˜

1) −𝑚(𝜒

˜

1) < 𝑚(𝑊) +𝑚(𝑏)

, the four-body decay channel ˜

˜

1

, where

and

are two fermions from the off-shell

decay, is assumed to occur (Figure 1(c)). In this search,

and

are a charged lepton and its associated anti-neutrino (or vice versa). For each of these two decay modes a dedicated event selection is performed to maximise the sensitivity. These selections are referred to as three-body and four-body selections in this paper. Direct pair production of top squarks which decay into an on-shell top quark and the lightest neutralino ˜

1→𝑡𝜒

˜

, will occur when

˜

1) −𝑚(𝜒

˜

1) > 𝑚(𝑡)

(Figure 1(d)). The signature of the

¯ +DM process is similar to that of the simplified model shown in Figure 1(a), so the same selection is also used to constrain the ˜

1 →𝑡𝜒

˜

model and it is referred to as the two-body selection.

The paper proceeds as follows; after a description of the ATLAS detector in Section 2, the data and simulated

Monte Carlo (MC) samples used in the analysis are detailed in Section 3 and the object identification

is documented in Section 4. The search strategy, the SM background estimations, and the systematic

uncertainties are discussed in Sections 5, 6 and 7. The results and their statistical interpretations are

presented in Sections 8 and 9. Finally, Section 10 presents the conclusions.

2 ATLAS detector

The ATLAS detector [42] at the LHC covers nearly the entire solid angle around the collision point.

It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer with three large superconducting toroidal magnets.

The inner-detector system (ID) is immersed in a 2 T axial magnetic field and provides charged-particle tracking in the range

2

5. The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track, the first hit normally being in the insertable B-layer installed before Run 2 [43, 44]. It is followed by the silicon microstrip tracker, which usually provides eight measurements per track. These silicon detectors are complemented by the transition radiation tracker (TRT), which enables radially extended track reconstruction up to

2

0. The TRT also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation.

The calorimeter system covers the pseudorapidity range

4

9. Within the region

3

2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering

1

8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillating-tile calorimeter, segmented into three barrel structures within

1

7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements respectively.

The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroids. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. A set of precision chambers covers the region

2

7 with three layers of monitored drift tubes, complemented by cathode-strip chambers in the forward region, where the background is highest. The muon trigger system covers the range

2

4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions.

Interesting events are selected to be recorded by the first-level trigger system implemented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [45].

The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger reduces in order to record events to disk at about 1 kHz.

3 Data and simulated event samples

The data used in this analysis were collected by the ATLAS detector during

collisions at a centre-of-mass energy of

√

𝑠 =

13 TeV from 2015 to 2018. The average number

of

interactions per bunch crossing (pile-up) varies from 14 during 2015 to 38 during 2017–2018. Only events taken in stable beam conditions,

2ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the𝑧-axis along the beam pipe. The𝑥-axis points from the IP to the centre of the LHC ring, and the𝑦-axis points upwards. Cylindrical coordinates(𝑟 , 𝜙)are used in the transverse plane,𝜙being the azimuthal angle around the𝑧-axis. The pseudorapidity is defined in terms of the polar angle𝜃as𝜂=−ln tan(𝜃/2), and the rapidity in terms of energy𝐸and momentum 𝑝as𝑦=0.5[(𝐸+𝑝_𝑧)/(𝐸−𝑝_𝑧)]. Angular distance is measured in units ofΔ𝑅≡√︁

(Δ𝑦)²+ (Δ𝜙)²orΔ𝑅_𝜂≡√︁

(Δ𝜂)²+ (Δ𝜙)². A vector energy𝐸®is defined by combining the energy deposited in the calorimeter with its deposit direction.

and for which all relevant detector systems were operational, are considered in this analysis. After data-quality requirements the data sample amounts to a total integrated luminosity of 139 fb

. The uncertainty in the combined 2015–2018 integrated luminosity is 1

7% [46], obtained using the LUCID-2 detector [47].

The two-body and three-body selections use events accepted by a trigger that requires a minimum of two electrons, two muons, or an electron and a muon [45]. Different trigger-level thresholds for the transverse momentum of the leptons were used in different data-taking periods, ranging between 8 and 22 GeV.

Tighter thresholds are applied in the lepton offline selection, to ensure that the trigger efficiency is ‘on plateau’ in all of the relevant kinematic region. Missing transverse momentum triggers [48] are used in the four-body selection to increase the acceptance of low-

T

leptons. The missing transverse momentum trigger threshold varied depending on data-taking conditions in the four years: 70 GeV for data collected during 2015; in the range 90–110 GeV for data collected during 2016, and 110 GeV for data collected during 2017 and 2018. Tighter offline requirements on the missing transverse momentum are defined accordingly to ensure event selection on the plateau region of the trigger efficiency curve.

Simulated event samples are used for SM background estimations and to model the signal samples.

Standard Model MC samples were processed through a full Geant4 [49] simulation of the ATLAS detector, while a fast simulation based on parameterisation of the calorimeter response and Geant4 simulation for all the other detector components [50] is used for the SUSY and DM signal samples. MC events are reconstructed using the same algorithms used for the data. To compensate for small residual differences between data and simulation in the lepton reconstruction efficiency, energy scale, energy resolution, trigger modelling, and

-tagging efficiency, the simulated events are reweighted using correction factors derived from data [51–53].

The events targeted by this analysis are characterised by two leptons with opposite electric charge, jets and missing transverse momentum. The main SM background contributions are expected to come from top quark pair production (

¯ ), associated production of a

boson and a top quark pair (

¯ ), single-top decay in the

production channel (

),

jets production and diboson processes (

with

).

Matrix element and showering generators used for the SM backgrounds and signals are listed in Table 1 along with the relevant parton distribution function (PDF) sets, the configuration of underlying-event and hadronisation parameters (tunes), and the cross-section order in

s

used to normalise the event yields.

Additional MC samples are used to estimate systematic uncertainties, as detailed in Section 7.

The SUSY top squark pair signal samples were generated from leading-order (LO) matrix elements with up to two extra partons using MadGraph5_aMC@NLO 2.6.2 [54]. MadGraph5_aMC@NLO was interfaced to Pythia 8.212 + MadSpin [55, 56] for the signal samples used in the three-body and four-body selections, while it was interfaced to Pythia 8.212 for the SUSY signal samples used for the interpretation of the two-body selection results. Signal cross-sections were calculated to next-to-next-to-leading order (NNLO) in

s

, adding the resummation of soft gluon emission at next-to-next-to-leading-logarithm

accuracy (NNLO+NNLL) [57–64]. The nominal cross section and the uncertainty are derived using the

PDF4LHC15 PDF set, following the recommendations presented in Ref. [65]. Jet–parton matching was

performed following the CKKW-L prescription [66]. The A14 tune [67] was used for the modelling

of parton showering, hadronisation and the underlying event. Parton luminosities were provided by the

NNPDF2.3LO PDF set [68].

𝑔_𝜒

) are set to one. The kinematics of the mediator decay are not strongly dependent on the values of the couplings; however, the particle kinematic distributions are sensitive to the nature of the mediator and to the mediator and DM particle masses. The cross-sections were computed at NLO [69, 70].

Inelastic

interactions were generated and overlaid onto the hard-scattering process to simulate the effect of multiple proton–proton interactions occurring during the same (in-time) or a nearby (out-of-time) bunch crossing. These were produced using Pythia 8.186 [71] and EvtGen [72] with the NNPDF2.3LO set of PDFs [68] and the A3 tune [73]. The MC samples were reweighted so that the distribution of the average number of interactions per bunch crossing reproduces the observed distribution in the data.

Table 1: Simulated signal and background event samples with the corresponding matrix element and parton shower (PS) generators, cross-section order in𝛼

sused to normalise the event yield, and the generator and PS PDF sets used.

Physics process Generator Parton shower Normalisation PDF (generator) PDF (PS)

SUSY Signals

MadGraph5_aMC@NLO [54]. Pythia 8.212 + MadSpin [55,56] NNLO+NNLL [57–64] NNPDF2.3LO [68] NNPDF2.3LO [68]

(three-body, four-body)

SUSY Signals (two-body) MadGraph5_aMC@NLO Pythia 8.212 NNLO+NNLL [57–64] NNPDF2.3LO NNPDF2.3LO DM Signals (two-body) MadGraph5_aMC@NLO Pythia 8.212 NLO [69,70] NNPDF2.3LO NNPDF2.3LO

𝑡¯𝑡 Powheg-Box v2 [74–76] Pythia 8.230 NNLO+NNLL [77] NNPDF3.0NLO [78] NNPDF2.3LO

𝑡¯𝑡+𝑉(𝑉=𝑊 , 𝑍) MadGraph5_aMC@NLO Pythia 8.210 NLO [54,79] NNPDF3.0NLO NNPDF2.3LO

Single top Powheg-Box v2 [74–76,80,81] Pythia 8.230 NLO+NNLL [82–86] NNPDF3.0NLO NNPDF2.3LO

𝑍/𝛾^∗(→ℓℓ)+jets Sherpa 2.2.1 [87,88] Sherpa 2.2.1 NNLO [89] NNPDF3.0NNLO [78] NNPDF3.0NNLO [78]

Diboson𝑉 𝑉(𝑉=𝑊 , 𝑍) Sherpa 2.2.1 or 2.2.2 [87] Sherpa 2.2.1 or 2.2.2 NLO [90] NNPDF3.0NNLO NNPDF3.0NNLO Triboson𝑉 𝑉 𝑉(𝑉=𝑊 , 𝑍) Sherpa 2.2.2 Sherpa 2.2.2 NLO [87,90] NNPDF3.0NNLO NNPDF3.0NNLO

𝑡¯𝑡 𝐻 Powheg-Box v2 [74,75,91] Pythia 8.230 NLO [54,79] NNPDF3.0NLO NNPDF2.3LO

𝑡¯𝑡𝑊 𝑊 MadGraph5_aMC@NLO Pythia 8.186 [71] NLO [54] NNPDF2.3LO NNPDF2.3LO

𝑡¯𝑡𝑊 𝑍 MadGraph5_aMC@NLO Pythia 8.212 NLO [54] NNPDF3.0NLO NNPDF2.3LO

𝑡 𝑍 , 𝑡𝑡 𝑡¯𝑡 , 𝑡¯ ¯𝑡 𝑡 MadGraph5_aMC@NLO Pythia 8.230 NLO [54] NNPDF3.0NLO NNPDF2.3LO

4 Object identification

Candidate events are required to have a reconstructed vertex with at least two associated tracks, each with

500 MeV and originating from the beam collision region in the

–

plane. The primary vertex in the event is the vertex with the highest scalar sum of the squared transverse momenta of associated tracks.

The leptons selected for analysis are classified as baseline or signal leptons depending on an increasingly stringent set of reconstruction quality criteria and kinematic selections, so that signal leptons are a subset of the baseline leptons. Baseline leptons are used in the calculation of missing transverse momentum (

T

), to resolve ambiguities between the analysis objects in the event, as described later, and for the fake/non-prompt (FNP) lepton background estimation described in Section 6. Signal leptons are used for the final event selection.

Baseline electron candidates are reconstructed from three-dimensional clusters of energy deposition in the electromagnetic calorimeter matched to ID tracks. These electron candidates are required to have pseudorapidity

2

47,

T >

4

5 GeV, and to pass a Loose likelihood-based identification requirement [51] with an additional condition on the number of hits in the B-layer. The tracks associated with electron candidates are required to have a longitudinal impact parameter

relative to the primary vertex

0

sin

0

5 mm, where

is the track’s polar angle.

3The transverse impact parameter is defined as the distance of closest approach in the transverse plane between a track and the beam-line. The longitudinal impact parameter corresponds to the𝑧-coordinate distance between the point along the track at which the transverse impact parameter is defined and the primary vertex.

Baseline muon candidates are reconstructed by matching ID tracks, in the pseudorapidity region

2

4 for the two-body and three-body selections and

2

7 for the four-body selection, with MS tracks or energy deposits in the calorimeter compatible with a minimum-ionising particle (calo-tagged muon). The resulting tracks are required to have a

T >

4 GeV and a

0

sin

0

5 mm from the primary vertex. Muon candidates are required to satisfy the Medium identification requirement, defined in Ref. [52], based on the numbers of hits in the different ID and MS subsystems, and on the significance of the charge-to-momentum ratio

.

Additional tighter selections are applied to the baseline lepton candidates to select the signal electrons or muons. Signal electrons are required to satisfy a Medium likelihood-based identification requirement [51]

and the track associated with a signal electron is required to have a significance

0|/𝜎(𝑑

0) <

5, where

0

is the transverse impact parameter relative to the reconstructed primary vertex and

0)

is its uncertainty.

Isolation criteria are applied to electrons by placing an upper limit on the sum of the transverse energy of the calorimeter energy clusters in a cone of size

(Δ𝜂)²+ (Δ𝜙)² =

0

2 around the electron (excluding the deposit from the electron itself) and the scalar sum of the

T

of tracks within a cone of

0

2 around the electron (excluding its own track). The isolation criteria are optimised such that the isolation selection efficiency is uniform across

. This varies from 90% for

T=

25 GeV to 99% for

60 GeV in events with a

boson decaying into pair of electrons [51].

For signal muons a significance in the transverse impact parameter

0|/𝜎(𝑑

0) <

3 is required. Isolation criteria applied to muons require the scalar sum of the

T

of tracks inside a cone of

0

3 around the muon (excluding its own track) to be less than 15% of the muon

T

. In addition, the sum of the transverse energy of the calorimeter energy clusters in a cone of

0

2 around the muon (excluding the energy from the lepton itself) must be less than 30% of the muon

T

[52].

Jets are reconstructed from three-dimensional clusters of energy in the calorimeter [92] using the anti-

jet clustering algorithm [93] as implemented in the FastJet package [94], with a radius parameter

0

4.

The reconstructed jets are then calibrated by the application of a jet energy scale derived from 13 TeV data and simulation [95]. Only jet candidates with

T >

20 GeV and

2

8 are considered.

To reduce the effects of pile-up, for jets with

2

5 and

T <

120 GeV a significant fraction of the tracks associated with each jet are required to have an origin compatible with the primary vertex, as defined by the jet vertex tagger (JVT) [96]. This requirement reduces the fraction of jets from pile-up to 1%, with an efficiency for pure hard-scatter jets of about 90%. Finally, in order to remove events impacted by detector noise and non-collision backgrounds, specific jet-quality requirements [97, 98] are applied, designed to provide an efficiency of selecting jets from proton–proton collisions above 99.5% (99.9%) for

20

100

GeV.

The MV2C10 boosted decision tree algorithm [53] identifies jets containing

-hadrons (‘

-jets’) by using quantities such as the impact parameters of associated tracks, and well-reconstructed secondary vertices. A selection that provides 77% efficiency for tagging

-jets in simulated

¯ events is used. The corresponding rejection factors against jets originating from

-quarks, from

-leptons, and from light quarks and gluons in the same sample at this working point are 4.9, 15 and 110, respectively.

To avoid reconstruction ambiguities and double counting of analysis objects, an overlap removal procedure

is applied to the baseline leptons and jets in the order which follows. First, the calo-tagged muons are

removed if sharing the track with electrons and, next, all electrons sharing an ID track with a muon are

and which lie within a cone of

(Δ𝑦)²+ (Δ𝜙)²=

0

2 around an electron candidate are removed. All jets lying within

0

2 of an electron are removed if the electron has

T >

100 GeV. Finally, any lepton candidate is removed in favour of a jet candidate if it lies a distance

min

0

4

0

04

10

T(ℓ))

from the jet, where

T(ℓ)

is the

T

of the lepton.

The missing transverse momentum (

T

), with magnitude

T

, is defined as the negative vector sum of the transverse momenta for all baseline electrons, photons, muons and jets. Low-momentum tracks from the primary vertex that are not associated with reconstructed analysis objects are also included in the calculation. The

T

value is adjusted for the calibration of the selected physics objects [99]. Linked to the

T

value is the ‘object-based

T

significance’, called simply ‘

T

significance’ in this paper.

This quantity measures the significance of

T

based upon the transverse momentum resolution of all objects used in the calculation of the

T

. It is defined as

T

significance

T |

√︃

𝜎2 L(

1

LT)

where

L

is the (longitudinal) component parallel to the

T

of the total transverse momentum resolution for all objects in the event and the quantity

LT

is the correlation factor between the parallel and perpendicular components of the transverse momentum resolution for each object. On an event-by-event basis, given the full event composition,

T

significance evaluates the

-value that the observed

T

is consistent with the null hypothesis of zero real

T

, as further detailed in Ref. [29]. In this way

T

significance helps to separate events with true

T

, arising from weakly interacting particles such as dark matter or neutralinos, from those where

T

is consistent with particle mismeasurement, resolution or identification inefficiencies, thus providing better background rejection.

5 Event selection

Different event selections are inspired by previous published strategies [27, 28] reoptimised to fully exploit the larger available dataset. For all selections, an improvement in the sensitivity is obtained with the introduction of the

T

significance variable, which enables further optimisation of the selection variables.

The four-body sensitivity also benefits from a reduction in the lepton

T

threshold in the region with small mass differences

˜

1,𝜒

˜

1)

between ˜

1

and ˜

1

. The threshold for the muon (electron)

T

was lowered from 7 GeV to 4 GeV (4

5 GeV).

Events are required to have exactly two signal leptons (two electrons, two muons, or one electron and one muon) with opposite electric charge. In the two-body and three-body selections, an invariant mass

greater than 20 GeV condition is applied to remove leptons from Drell–Yan and low-mass resonances, while in the four-body selection, given the softer

T

spectrum of the leptons,

is required to be higher than 10 GeV. Events with same flavour (SF) lepton pairs (

and

) with

between 71.2 and 111.2 GeV are rejected to reduce the

boson background, except for the four-body selection. No additional

selection is imposed on the different flavour (DF) lepton pairs (

). Different jet (

-jet) multiplicities, labelled as

jets

(

jets

), are required in the three selections, as detailed below.

5.1 Discriminators and kinematic variables

Final event selections are obtained by separating signal from SM background using different kinematic variables. Two variables are constructed from the

T

and the

T

of the leading leptons and jets:

𝑅2ℓ=𝐸^miss

T /(𝑝

T(ℓ

1) +𝑝

T(ℓ

2))

and

2ℓ4𝑗 =𝐸^miss

T / 𝐸^miss

T +𝑝

T(ℓ

1) +𝑝

T(ℓ

2) + ∑︁

𝑖=1, ..., 𝑁≤4

𝑝T(𝑗_𝑖)

!

where

T(ℓ

1)

and

T(ℓ

2)

are the leading and sub-leading lepton transverse momenta respectively and

1, ..., 𝑁≤4)

are the transverse momenta of the up to four leading jets, in decreasing order. For some backgrounds, e.g.

jets, the variable

2ℓ

has a distribution that peaks at lower values than the signal, and it is thus used to reject those backgrounds. Similarly,

2ℓ4𝑗

is employed for its high rejection power against multi-jet events.

Another variable employed is

T,boost

, which is defined as the vectorial sum of

T

and the leptons’

transverse momentum vectors

1)

and

2)

. Its magnitude,

T,boost

, can be interpreted as the magnitude of the vector sum of all the transverse hadronic activity in the event. The azimuthal angle between the

T

vector and the

T,boost

vector is defined as

boost

. This variable is useful for selecting events where the non hadronic component (

,

,

and

or ˜

1

) is collimated.

The lepton-based stransverse mass [100, 101] is a kinematic variable used to bound the masses of a pair of identical particles which have each decayed into a visible and an invisible particle. This quantity is defined as

𝑚T2(p_T,1,p_T,2,p^miss

T ) =

min

q_T,1+q_T,2=p^miss T

max

T(p_T,1,q_T,1), 𝑚

T(p_T,2,q_T,2) ] ,

where

T

indicates the transverse mass,

and

are the transverse momentum vectors of two visible particles, and

and

are transverse momentum vectors with

T =q_T,1+q_T,2

. The minimisation is performed over all the possible decompositions of

T

. In this paper,

and

are the transverse momentum vectors of the two leptons and

T2(p_T(ℓ

1),p_T(ℓ

2),p^miss

T )

is referred to simply as

T2

. For the

T2

calculation, the invisible particles are assumed to be massless. The

T2

distribution is expected to have an endpoint corresponding to the

mass for backgrounds such as

¯ while it is expected to reach higher values in the case of SUSY events, due to the presence of the neutralinos [102, 103].

The three-body selection uses a number of ‘super-razor’ variables [104], which are derived with a series of assumptions made in order to approximate the centre-of-mass energy frame (Razor Frame) of two parent particles (i.e. top squarks) and the decay frames. Each parent particle is assumed to decay into a set of visible (only leptons are considered in this case) and invisible particles (i.e. neutrinos and neutralinos).

These variables are

T

, the Lorentz factor

R+1

, the azimuthal angle

𝛽

and

Δ

. The first variable is

T=| ®𝐽

T|/(| ®𝐽

T| +√

ˆ

𝑠R/

4

with

T

as the vector sum of the transverse momenta of the visible particles and the missing transverse momentum, and

√

ˆ

𝑠R

as an estimate of the system’s energy in the razor frame

, defined as the frame in which the two visible leptons have equal and opposite longitudinal momentum (

z

). The value of

T|

vanishes for events where leptons are the only visible particles, such as diboson events, leading to

T

values that tend toward zero. Instead, in events that contain additional activity, such as

¯ , this variable tends towards unity. The Lorentz factor,

R+1

, is associated with the boost from the

razor frame

to the approximation of the two decay frames of the parent particles and is expected to have

values tending towards unity for back-to-back visible particles or when they have different momenta. Lower values of

R+1

are otherwise expected when the two visible particles are collinear and have comparable momentum. The azimuthal angle

𝛽

is defined between the razor boost from the laboratory to the

frame and the sum of the visible momenta as evaluated in the

frame. It is a good discriminator when used in searches for signals from models with small mass differences between the massive pair-produced particle and the invisible particle produced in the decay. Finally, the last variable is

Δ =√

ˆ

R+1

, which is particularly powerful in discriminating between signal events and

¯ and diboson background, since it has a kinematic end-point that is proportional to the mass-splitting between the parent particle and the invisible particle.

5.2 Two-body event selection

This selection targets the dark-matter signal model that assumes the production of a pair of dark-matter particles through the exchange of a spin-0 mediator, in association with a pair of top quarks (Figure 1(a)).

It is also used for a search for top squarks decaying into an on-shell top and neutralino (Figure 1(d)).

For each event, the leading lepton,

1

, is required to have

T(ℓ

1) >

25 GeV, while for the sub-leading lepton,

2

, the requirement is

T(ℓ

2) >

20 GeV. The event selection also requires at least one reconstructed

-jet,

boost

lower than 1.5 and

T

significance greater than 12, and finally

T2

greater than 110 GeV.

Following the classification of the events, two sets of signal regions (SRs) are defined: a set of exclusive SRs binned in the

T2

variable, to maximise model-dependent search sensitivity, and a set of inclusive SRs, to be used for model-independent results. For the binned SRs, events are separated according to the lepton flavours, different flavour or same flavour, and by the range

of the

T2

interval: SR

DF

or SR

SF

. For the inclusive signal regions, referred to as SR

with

being the lower bound placed on the

T2

variable, DF and SF events are combined. The common definition of these two sets of signal regions is shown in Table 2.

Table 2: Two-body selection. Common definition of the binned and the inclusive sets of signal regions.

SR

Leptons flavour DF SF

𝑝T(ℓ

1)

[GeV]

25

𝑝T(ℓ

2)

[GeV]

20

𝑚_{ℓ ℓ}

[GeV]

20

|𝑚_{ℓ ℓ}−𝑚_𝑍|

[GeV] –

20

jets ≥

1

Δ𝜙

boost

[rad]

1

5

T

significance

12

T2

[GeV]

110

5.3 Three-body event selection

The three-body decay mode of the top squark shown in Figure 1(b) is dominant in the region where

˜

1) > 𝑚(𝜒

˜

1) +𝑚(𝑊) +𝑚(𝑏)

and

˜

1) < 𝑚(𝜒

˜

1) +𝑚(𝑡)

. The signal kinematics in this region resemble that of

production when

˜

˜

1) ∼𝑚(𝑊)

and that of

¯ production when

˜

˜

1) ∼𝑚(𝑡)

. The signal selection was optimised to reject these dominant backgrounds while not degrading signal efficiency.

The

-jet multiplicity is highly dependent on the mass-splitting between the top squark and the neutralino,

˜

1,𝜒

˜

1) =𝑚(𝑡

˜

1) −𝑚(𝜒

˜

1)

, since for lower

˜

1,𝜒

˜

1)

the

-jets have lower momentum and cannot be reconstructed efficiently. Accordingly, two orthogonal signal regions were defined: SR

targeting

˜

˜

1) ∼𝑚(𝑊)

, applying a

-jet veto, and SR

targeting

˜

˜

1) ∼𝑚(𝑡)

, allowing for

-jets.

Separation between same-flavour and different-flavour events is also kept to optimise model-dependent search sensitivity, thus defining four different SRs: SR-DF

, SR-SF

, SR-DF

and SR- SF

. The signal regions make use of a common set of requirements on the

T

of the two leptons,

T

significance and

R+1

. The definitions of these regions are summarised in Table 3.

Table 3: Three-body selection. Signal regions definition.

SR

SR

Leptons flavour DF SF DF SF

𝑝T(ℓ

1)

[GeV]

25

25

𝑝T(ℓ

2)

[GeV]

20

20

𝑚_{ℓ ℓ}

[GeV]

20

20

|𝑚_{ℓ ℓ}−𝑚_𝑍|

[GeV] –

20 –

20

jets =

0

1

Δ𝜙R

𝛽

[rad]

2

3

2

3

𝐸miss

T

significance

12

12

1/

R+1 >

0

7

0

7

𝑅_𝑝

T

>

0

78

0

70

Δ

[GeV]

105

120

5.4 Four-body event selection In the kinematic region defined by

˜

1) < 𝑚(𝜒

˜

1) +𝑚(𝑏) +𝑚(𝑊)

and

˜

1) > 𝑚(𝜒

˜

1) +𝑚(𝑏)

, the top squarks are assumed to decay via a four-body process through an off-shell top quark and

boson as shown in Figure 1(c). In this region the final-state leptons from the virtual

boson decay are expected to have lower momentum and can be efficiently selected when imposing both a lower and upper bound on the

T

of the leptons. A transverse momentum lower bound of 4.5 GeV (4 GeV) is applied for electrons (muons), together with an upper bound, which is optimised separately for the leading and the sub-leading leptons.

Two separate signal regions are defined to cover different

˜

1,𝜒

˜

1)

ranges: the first one, SR

,

ensures orthogonality between the two SRs. The presence of an energetic initial-state radiation (ISR) jet recoiling against the system of the two top squarks is required, introducing an imbalance in the event kinematics with an enhanced value of

T

that allows signal events to be distinguished from SM processes.

For this reason, for each event, the leading jet

1

is considered to be a jet from ISR and required to have

150 GeV. A further reduction of the SM background is achieved with selections on

T

significance,

T,boost

,

2ℓ

and

2ℓ4𝑗

variables. An additional requirement is applied to improve the sub-leading lepton isolation, using the following isolation variable:

min

2, 𝑗_𝑖 =

min

𝑗𝑖∈ [jets]Δ𝑅_𝜂(ℓ

2, 𝑗_𝑖)

where ‘[jets]’ contains all the jets in the event. This reduces the probability of lepton misidentification or selecting a lepton originating from heavy-flavour or

decays in jets. The definitions of these regions are summarised in Table 4.

Table 4: Four-body selection. Signal regions definition.

SR

SR

𝑝T(ℓ

1)

[GeV]

25

100

𝑝T(ℓ

2)

[GeV]

10

10

50

𝑚_{ℓ ℓ}

[GeV]

10

𝑝T(𝑗

1)

[GeV]

150

min

2, 𝑗_𝑖 >

1

𝐸miss

T

significance

10

𝑝^{ℓ ℓ}

T,boost

[GeV]

280

𝐸miss

T

[GeV]

400

𝑅2ℓ >

25

13

𝑅2ℓ4𝑗 >

0

44

0

38

6 Background estimation

The MC predictions for the dominant SM background processes are improved using a data-driven normalisation procedure, while non-dominant processes are estimated directly using MC simulation.

A simultaneous profile likelihood fit [105] is used to constrain the MC yields with the observed data in dedicated background control regions (CRs). The fit is performed using standard minimisation software [106, 107] where the normalisations of the targeted backgrounds are allowed to float, while the MC simulation is used to describe the shape of kinematic variables. Systematic uncertainties that could affect the expected yields in the different regions are taken into account in the fit through nuisance parameters. Each uncertainty source is described by a single nuisance parameter, and correlations between nuisance parameters, background processes and selections are taken into account. A list of the systematic uncertainties considered in the fits is provided in Section 7. The SM background thus modelled is validated in dedicated validation regions (VRs) which are disjoint from both the control and signal regions.

Important sources of reducible background are events with jets which are misidentified as leptons. The

fake/non-prompt (FNP) lepton background comes from

and heavy-flavour hadron decays and photon

conversions. This is particularly important for the low-

T

leptons targeted by the four-body selection.

The FNP background is mainly suppressed by the lepton isolation requirements described in Section 4, but a non-negligible residual contribution is expected. This is estimated from data using the ‘fake factor’

method [108–111] which uses two orthogonal lepton definitions, labelled as ‘Id’ and ‘anti-Id’, to define a control data sample enriched in fake leptons. The Id lepton corresponds to the signal lepton identification criteria used in this analysis. Anti-Id electrons fail either the signal identification or isolation requirement, while anti-Id muons fail the isolation requirement. The sample used for the fake-factor computation is enriched in

+jets events. Events with three leptons are selected, with the two same-flavour leptons of opposite electric charge (SFOS leptons) identified as the

boson decay products (

1

and

2

, in order of decreasing

T

) satisfying the Id requirements, and the third unpaired lepton, called the probe lepton (

), satisfying either the Id or anti-Id criteria. The fake factor is defined as the ratio of the Id lepton yield to the anti-Id probe lepton yield. Residual contributions from processes producing prompt leptons are subtracted using the MC predictions. Fake factors are measured separately for electrons and muons and as a function of the lepton

T

and

. These are derived in the CR

region whose selection is summarised in Table 5. The FNP estimates in each analysis region are derived by applying the fake factors to events satisfying that region’s criteria but replacing at least one of the signal leptons by an anti-Id one.

Table 5: FNP selection. Detailed definition of the CR^FNPregion.

CR

Lepton multiplicity 3

|𝑚_{ℓ ℓ}−𝑚_𝑍|

[GeV]

10 for SFOS pair

1)

[GeV]

25

𝑝T(ℓ^𝑍

2)

[GeV]

20

𝑝T(ℓ^probe)

[GeV]

4

5

4

0

0

2

T )

[GeV]

40 Additional requirements

𝑝T(ℓ^probe) <

16 GeV or

𝐸miss T

<

50 GeV

The three selections in this paper use different sets of CRs and VRs, specifically designed to be kinematically similar to the respective SRs. The definitions of the regions used in each analysis and the results of the fits are described in the following subsections.

6.1 Estimation of the backgrounds in the two-body selection

The main background sources for the two-body selection are

¯ and

¯ with invisible decay of the

boson.

These processes are normalised to data in dedicated CRs: CR

and CR

. The

¯ normalisation

factor is extracted from different-flavour dilepton events. In order to test the reliability of the

¯ background

prediction, two validation regions VR

and VR

are defined. The

¯ production events with

invisible decay of the

boson are expected to dominate the tail of the

distribution in the SRs and

final state is adopted. Events are selected if characterised by three charged leptons including at least one pair of SFOS leptons having invariant mass consistent with that of the

boson (

20 GeV).

If more than one pair is identified, the one with

closest to the

boson mass is chosen. Events are further required to have a jet multiplicity,

jets

, greater than or equal to three with at least two

-tagged jets. These selections target

¯ production with the

boson decaying into two leptons and

¯ decaying in the semileptonic channel. In order to select

¯ events whose kinematics, regardless of subsequent

¯ and

decays, emulate the kinematics of this background in the SRs, the momenta of the two leptons of the SFOS pair

1),p(ℓ^Z

2))

are vectorially added to the

T

, effectively treating them like the neutrino pair from the

boson decay. A variable called

T,corr= p^miss

T +p(ℓZ

1) +p(ℓZ 2)

T

is constructed. Events characterised by high

T2

in the SRs are emulated by requiring high

T,corr

values in CR

. In order to check the

¯ background estimation, the validation region VR

was defined. For this region, events with four leptons are selected and required to have at least one pair of SFOS leptons compatible with the

boson decay. A variant of the

T2

variable called

T2

is defined from the

T,corr= p^miss

T +p(ℓZ

1) +p(ℓZ 2)

T

and the momenta of the remaining two leptons. The definition of the control and validation regions used in the two-body selection is summarised in Table 6. The expected signal contamination in the CRs is generally below

1%. The signal contamination in the VRs is less than 15% (7%) for a DM signal model with scalar (pseudoscalar) mediator mass of 100 GeV and DM mass of 1 GeV.

Table 6: Two-body selection. Control and validation regions definition. The common selection defined in Section5 also applies to all regions.

CR^2−body𝑡𝑡¯ CR^𝑡𝑡 𝑍¯ VR^2−body𝑡𝑡 ,¯DF VR^2−body𝑡𝑡 ,¯SF VR^2−body𝑡𝑡 𝑍¯

Lepton multiplicity 2 3 2 4

Lepton flavour DF at least one SFOS pair DF SF at least one SFOS pair

𝑝T(ℓ

1)[GeV] >25 >25 >25 >25

𝑝T(ℓ

2)[GeV] >20 >20 >20 >20

𝑝T(ℓ

3)[GeV] – >20 – >20

𝑝T(ℓ

4)[GeV] – – – >20

𝑚_{ℓ ℓ} >20 – >20 –

|𝑚_{ℓ ℓ}−𝑚_𝑍|[GeV] – <20 for at least one SFOS pair – >20 <20 for the SFOS pair

𝑛_𝑏−jets ≥1 ≥2 with𝑛

jets≥3 ≥1 >0

Δ𝜙

boost[rad] ≥1.5 – <1.5 –

𝐸miss

T significance >8 – >12 –

𝐸^miss

T,corr[GeV] – >140 – –

𝑚^{ℓ ℓ}

T2 [GeV] [100, 120] – [100, 110] –

𝑚^4ℓ

T2 [GeV] – – – >110

Figure 2 illustrates the modelling of the shape of two important variables after the background fit: (a) shows the

boost

distribution with the CR

selection, and (b) shows the

distribution of the SFOS leptons in the CR

selection. Good agreement is found between the data and the background model for all of the selection variables.

The results of the fit are reported in Table 7 for the two-body CRs and VRs. The normalisations for fitted backgrounds are found to be consistent with the theoretical predictions when uncertainties are considered:

the normalisation factors obtained from the fit for

¯ and

¯ are 0

88

0

08 and 1

07

0

14 respectively.